Automatic marking vehicle self-adaptive control method based on mechanism and data driven model

Abstract

The automatic marking vehicle adaptive control method based on mechanism and data-driven model of the application comprises the following steps: a) firstly, a kinematic model equation of the marking vehicle is established, then a marking vehicle motion model based on mechanism and data driving is established, and finally the motion model is linearized; b) the recursive least squares method is used to recursively estimate and identify the parameters in the system, and with the generation of new observation data, the parameter estimation is recursively corrected until the parameter estimation reaches the required accuracy; c) the controller for path tracking is realized by controlling the vehicle speed v and the front wheel angle, with the minimum vehicle position and reference path point position error as the control target. The automatic marking vehicle adaptive control method based on mechanism and data-driven model of the application can not only improve the marking efficiency and quality, save the construction cost, shorten the construction period, but also provide data support for the later work such as road marking maintenance.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of automatic marking car driving track control method, more specifically, and especially, it is a kind of automatic marking car adaptive control method based on mechanism and data-driven model. BACKGROUND

[0002] In the context of automatic marking car, path tracking control is an important part of automatic marking car, which is used to follow the predetermined guide line to mark road marking. Path tracking control involves using sensors and control algorithms to guide the vehicle to travel along the desired path. The control algorithm adjusts the steering and throttle according to the information obtained from the sensor, so that the vehicle remains on the track.

[0003] PID control, modern control and intelligent control methods are widely used in unmanned driving. Researchers have proposed various improved algorithms to improve the performance and stability of the controller, such as using dead zone compensator to overcome dead zone, multi-swarm intelligence fusion optimization algorithm, adaptive MIMO-PID controller based on reinforcement learning, etc. In addition, some researchers use data-driven methods for adaptive control, such as data-driven adaptive automatic parking scheme and using machine learning to realize path tracking control of car, etc. These researches aim to further improve the accuracy and efficiency of path tracking control.

[0004] Sliding mode control and model predictive control methods are also commonly used for vehicle path tracking. Sliding mode control (SMC) is a widely used control type, but it has the problem of chattering. To solve this problem, researchers have proposed some methods. For example, some scholars have proposed using saturation function to reduce chattering, while other scholars have proposed an adaptive control law combining radial basis function neural network (RBF) and sliding mode control, which reduces the switching gain to improve the stability of the control system, especially in the presence of random disturbances and parameter perturbations. These methods can be applied to unmanned driving platforms to improve the accuracy and stability of mobile robot and vehicle platform path tracking control. Model predictive controller (MPC) is a commonly used control method that uses linear or nonlinear models to predict the state of the controlled object. MPC controller requires a large amount of computing resources, so heuristic methods are needed to solve optimization problems.

[0005] Intelligent technologies such as fuzzy control theory and neural networks are widely used in vehicle lateral stability control systems. Fuzzy control and neural network control are both control methods based on non-traditional control theory, which can be applied to systems with uncertainty and complexity. Fuzzy control uses fuzzy rules and fuzzy reasoning for control, which can handle the nonlinear relationship between input and output. Neural network control uses the learning and adaptability of neural networks to achieve control, which can learn the dynamic characteristics of the system and adapt to system changes.

[0006] The existing relatively advanced path tracking control method is mostly based on the vehicle dynamics or kinematics model to design a tracking controller, but the vehicle generally has high nonlinearity, time-varying characteristics and other characteristics, and it is difficult to obtain an accurate model thereof, and for the tracking control method based on data driving, the convergence and reliability of the control system cannot be guaranteed due to the lack of constraints of the vehicle operation mechanism.

[0007] In view of the problems that there are errors between the mechanism model and the automatic marking vehicle, and the data-driven modeling is affected by the fluctuation of the collected data, a vehicle motion model based on mechanism model and data driving is provided. The vehicle mechanism model is used as the prior knowledge of the data-driven model, the state predicted by the mechanism model is compared with the actual data, so as to obtain the error between the mechanism model and the actual vehicle. Then, the error is compensated by using an active regression (Auto-Regressive with Extra Inputs, ARX) model, so as to obtain a more accurate vehicle motion state prediction result. In addition, the parameter identification method of the ARX model is improved, and the parameter variation limit weight item in the performance index function of the commonly used least square method.

[0008] In view of the problems that there are errors between the mechanism model and the automatic marking vehicle, and the data-driven modeling is affected by the fluctuation of the collected data, a vehicle motion model based on mechanism model and data driving is provided. The vehicle mechanism model is used as the prior knowledge of the data-driven model, the state predicted by the mechanism model is compared with the actual data, so as to obtain the error between the mechanism model and the actual vehicle. Then, the error is compensated by using an active regression (Auto-Regressive with Extra Inputs, ARX) model, so as to obtain a more accurate vehicle motion state prediction result. In addition, the parameter identification method of the ARX model is improved, and the parameter variation limit weight item in the performance index function of the commonly used least square method. SUMMARY

[0009] The present application provides an automatic marking vehicle adaptive control method based on mechanism and data-driven model.

[0010] The automatic marking vehicle adaptive control method based on mechanism and data-driven model of the present application is characterized in that it is realized by the following method:

[0011] a. Establishment of a marking vehicle model based on mechanism and data driving; first, a kinematics model equation of the marking vehicle is established according to the mechanism model of the marking vehicle, then a marking vehicle motion model based on mechanism and data driving is established, and finally the marking vehicle motion model is linearized;

[0012] b. Parameter estimation based on data-driven error compensation model; recursive least squares method is used to recursively estimate and identify the parameters in the system, and with the generation of new observation data, the parameter estimation is recursively corrected until the parameter estimation reaches the required accuracy;

[0013] c) Adaptive path tracking controller design; with the control objective of minimizing the position error between the vehicle and the reference path point, the controller controls the vehicle speed v and the front wheel steering angle δ. f A controller that implements path tracking, wherein the position error includes the lateral and longitudinal coordinate errors of the vehicle relative to the reference trajectory and the heading angle error.

[0014] The adaptive control method for an automatic lane marking vehicle based on a mechanism and data-driven model of the present invention is implemented through the following steps in step a):

[0015] a-1). Establish the kinematic equations of the lane-marking vehicle; the front wheels of the lane-marking vehicle are the steering wheels, and the trajectory of the midpoint of the rear axle is selected to represent the vehicle's trajectory. In the vehicle's motion plane, establish a planar coordinate system O-XY, where x and y represent the abscissa and ordinate of the midpoint of the rear axle, respectively, v represents the vehicle velocity, ψ represents the vehicle body angle, and δ... f Let L represent the front wheel steering angle, and L represent the wheelbase between the front and rear wheels; establish the kinematic model equations of the marked car as shown in formula (1):

[0016]

[0017] Since microprocessors process digital signals in practical applications, the vehicle kinematics model in formula (1) is discretized:

[0018]

[0019] Where T represents the control period;

[0020] Based on the vehicle steering control mechanism, it is known that during actual parking, the front wheel steering angle will be affected by the maximum rotation angle of the front wheels. Due to the limitations, the front wheel steering angle in formula (2) must satisfy the following constraints:

[0021] a-2). Establish a motion vehicle model based on mechanism and data-driven approach; since the mechanism model makes some assumptions, ignores some factors, and is discretized, there is an error between the vehicle mechanism model and the actual vehicle; therefore, a combination of vehicle mechanism model and data-driven modeling is adopted, and the data-driven method is used to compensate for this error.

[0022] make U(k) is the output of the mechanism- and data-driven motion vehicle model at time k, and U(k) is the input of the mechanism- and data-driven motion vehicle model at time k. Let k+1 be the model estimation error; then the mechanism model is the same as... The function related to U(k) is expressed as: The error compensation model is the same as The function related to U(k) is expressed as: Establish a mechanism and data-driven vehicle model as shown in formula (3):

[0023]

[0024] In the formula, The predicted output for a mechanism- and data-driven moving vehicle model;

[0025] a-3). Establishment of ARX kinematic model; Error compensation of vehicle kinematic model is performed using time series ARX model. The general structure of the ARX model of kinematic model and actual vehicle output error is as follows:

[0026]

[0027] in, Let U(k) be the output error of the vehicle kinematics model at time k, and U(k) = [v(k), δ f (k)] T , is the input at time k; n a and n b These correspond to the orders of the input and output, respectively; A i (k+1) is a 3×3 matrix, B j (k+1) is a 3×2 matrix.

[0028]

[0029] Among them, A i (k+1), B j (k+1) is an unknown parameter;

[0030] From the above, the motion vehicle model based on mechanism and data-driven principles can be represented as follows:

[0031]

[0032] a-4). Linearization of the vehicle kinematics model; Since the vehicle kinematics model established by formula (2) contains nonlinear terms, which is not conducive to the design and solution of the controller, the nonlinear terms in formula (2) are linearized. The linear form of formula (2) can be expressed as:

[0033]

[0034] Where Y(k+1) is the predicted output of the linearized vehicle kinematics model, Y(k)=[x(k),y(k),ψ(k)] T For time k, the output is U(k) = [v(k), δ f(k)] T is the input at time k, C(k) are the parameter matrix and time-varying constant matrix after linearization of the model, respectively;

[0035] The vehicle motion model established by formula (2) is expressed as:

[0036]

[0037] Let g(v(k),δ f (k)) be the first-order Taylor expansion at (v(k-1),δ f (k-1)):

[0038]

[0039] Therefore, formula (7) can be expressed as:

[0040]

[0041] Therefore C(k) is expressed as follows:

[0042]

[0043]

[0044] The automatic marking vehicle adaptive control method based on mechanism and data-driven model of the present application is realized by the following steps in step b) based on data-driven error compensation model parameter estimation:

[0045] b-1). The least squares form of formula (4) is expressed as follows:

[0046]

[0047] Wherein, φ(k) is the observation data vector, θ is the parameter vector to be estimated, and:

[0048]

[0049] b-2). In order to prevent the parameter from changing too much, a parameter change weight term is added on the basis of the recursive least squares forgetting factor method, η>0, which is a weight factor used to limit the change of the estimated parameter;

[0050] The performance index is taken as:

[0051]

[0052] Let Then we can get:

[0053]

[0054] The least squares estimation problem of the parameters is to minimize the objective function (16) by finding the minimum value of J with respect to J. The first derivative of is set to zero, i.e.:

[0055]

[0056] By solving equation (16), we can obtain The value is given by the following formula:

[0057]

[0058] Let μ = β 2 If 0 < μ ≤ 1, then the least squares estimated parameters are... The solution is:

[0059]

[0060] make Discuss the factors in formula (18):

[0061] P -1 (k)=η-μη+μ·P -1 (k-1)+φ(k)φ T (k) (19)

[0062]

[0063] b-3). According to (18), the following formula can be obtained:

[0064]

[0065] Multiply both sides of formula (21) by the left side. The formula is as follows:

[0066]

[0067] Substituting (19) into (18) gives:

[0068]

[0069] Substituting (20) into formula (23) yields:

[0070]

[0071] Substituting (22) into formula (24) yields:

[0072]

[0073] Substituting (21) into formula (25) yields:

[0074]

[0075] The improved formula of the forgetting factor recursive least square parameter estimation is as follows:

[0076]

[0077] The adaptive control method of the automatic marking vehicle based on the mechanism and data-driven model comprises the following steps:

[0078] c-1). The vehicle linear system discrete model can be expressed as:

[0079]

[0080] c-2). The change rate of the vehicle speed and the steering will affect the stability of the system, so the change of the controller input needs to be limited; if the one-step forward prediction error criterion function is used, the control input solved by minimizing the function will be too large, at this time, the controller cannot realize the stable control of the system and the stability of the control system itself will be destroyed; therefore, in order to solve the above problems, the following input criterion is designed:

[0081]

[0082] Wherein, λ>0 is a weight factor for limiting the change of the control input; Y * (k+1) is a target trajectory point and an expected heading angle, is the maximum vehicle speed and the front wheel steering angle;

[0083] c-3). The formula (28) is substituted into the formula (29) to obtain:

[0084]

[0085] The formula (30) is derived with respect to U(k):

[0086]

[0087] In the formula (31), The solving method is shown in the formula (10) and the formula (11), A i (k+1) is a 3*3 matrix, A i (k+1) is a 3*3 matrix, B i (k+1) is a 3*2 matrix, n a =2, n b =2, then the following can be obtained:

[0088]

[0089] Let Then, the control rate can be obtained as formula (34):

[0090]

[0091] Further, the control rate can be obtained as formula (34):

[0092]

[0093] The beneficial effects of the present application are: the automatic marking vehicle adaptive control method based on mechanism and data-driven model of the present application proposes a vehicle motion model based on mechanism model and data-driven, the vehicle mechanism model is used as the priori knowledge of the data-driven model, the state predicted by the mechanism model is compared with the actual data, so as to obtain the error between the mechanism model and the actual vehicle; then, the error is compensated by using an active regression (Auto-Regressive with Extra Inputs, ARX) model, so as to obtain a more accurate vehicle motion state prediction result. The automatic marking vehicle adaptive control method of the present application not only can improve the marking efficiency and quality, save the construction cost, shorten the construction period, but also can provide data support for the later work such as road marking maintenance. BRIEF DESCRIPTION OF DRAWINGS

[0094] Figure 1 It is a kinematic model diagram of the marking vehicle established in the present application;

[0095] Figure 2 It is a system block diagram of the automatic marking vehicle adaptive control method of the present application;

[0096] Figure 3 It is a model structure diagram of the automatic marking vehicle adaptive control method of the present application;

[0097] Figure 4 It is a control effect diagram of the automatic marking vehicle adaptive control method of the present application for straight line path tracking;

[0098] Figure 5 It is a control effect diagram of the automatic marking vehicle adaptive control method of the present application for curve path tracking;

[0099] Figure 6 It is a control effect diagram of the MFAC algorithm for straight line path tracking;

[0100] Figure 7 It is a control effect diagram of the MFAC algorithm for curve path tracking;

[0101] Figure 8 It is a control effect diagram of the MFAC algorithm for straight line path tracking based on coordinate compensation;

[0102] Figure 9 The control effect diagram of the curve path tracking of the MFAC algorithm based on coordinate compensation;

[0103] Figure 10 The curve path tracking control effect diagram of the automatic line marking vehicle adaptive control method of the present application without noise;

[0104] Figure 11 The curve path tracking control effect diagram of the MFAC algorithm based on coordinate compensation without noise;

[0105] Figure 12 The path tracking control deviation diagram of the automatic line marking vehicle adaptive control method of the present application without noise;

[0106] Figure 13 The path tracking control deviation diagram of the MFAC algorithm based on coordinate compensation without noise;

[0107] Figure 14 The path tracking control deviation diagram of the automatic line marking vehicle adaptive control method of the present application with disturbance noise;

[0108] Figure 15 The path tracking control deviation diagram of the MFAC algorithm based on coordinate compensation with disturbance noise

[0109] Figure 16 The path tracking control output diagram of the automatic line marking vehicle adaptive control method of the present application with disturbance noise;

[0110] Figure 17 The path tracking control output diagram of the MFAC algorithm based on coordinate compensation with disturbance noise. DETAILED DESCRIPTION

[0111] The present application will be further described below in conjunction with the accompanying drawings and examples.

[0112] As shown in Figure 1 , the kinematic model diagram of the line marking vehicle established in the present application is given. Since the motion speed of the automatic line marking vehicle is low, and the rear wheel is a non-steering wheel, it is not easy to appear side slip phenomenon, therefore the motion trajectory of the midpoint of the rear axle is selected to replace the motion trajectory of the vehicle, and the kinematic model of the line marking vehicle as shown in Figure 1 is established.

[0113] As shown in Figure 2As shown in the figure, the system block diagram of the adaptive control method of the automatic marking vehicle of the application is given, and the path tracking adaptive control scheme designed by the application is based on the mechanism model compensated by data-driven error. First, the structure of the vehicle mechanism model is determined, then the error compensation model based on data-driven is established, the improved recursive least square forgetting factor method is used to estimate the error according to the past data, and then the estimated error is used to compensate the mechanism model. As shown in the figure, Figure 1 As shown in the figure, the vehicle provides data for the error compensation model according to the actual state measured by the sensor and the state output by the model, and the mechanism model is compensated to obtain the corrected control system model, and the optimal control amount at each time is calculated by the adaptive controller. According to the vehicle mechanism model corrected online according to the model error, the dynamic changes of the system in the actual control can be well considered, and the robustness is high.

[0114] The adaptive control method of the automatic marking vehicle based on the mechanism and data-driven model of the application is realized by the following method:

[0115] a). Establishment of the marking vehicle model based on mechanism and data driving; first, the kinematic model equation of the marking vehicle is established according to the mechanism model of the marking vehicle, then the marking vehicle motion model based on mechanism and data driving is established, and finally the marking vehicle motion model is linearized;

[0116] The establishment of the marking vehicle model based on mechanism and data driving is realized by the following steps:

[0117] a-1). Establish the kinematic equation of the marking vehicle; the front wheel of the marking vehicle is a steering wheel, the motion trajectory of the midpoint of the rear axle of the marking vehicle is selected to replace the motion trajectory of the vehicle, a plane coordinate system O-XY is established in the motion plane of the vehicle, x and y represent the horizontal coordinate and vertical coordinate of the midpoint of the rear axle of the vehicle respectively, v represents the vehicle speed, ψ represents the body angle, δ f represents the front wheel steering angle, and L represents the wheelbase between the front and rear wheels; the kinematic model equation of the marking vehicle is established as shown in formula (1):

[0118]

[0119] Because the microprocessor processes signals in actual application are all digital signals, the kinematic model of the vehicle in formula (1) is discretized:

[0120]

[0121] Wherein, T represents the control period;

[0122] According to the vehicle steering control mechanism, it can be known that in the actual parking process, the front wheel steering angle will be limited by the maximum rotation angle of the front wheel The front wheel steering angle in formula (2) needs to meet the constraint condition:

[0123] a-2). Establish a mechanism and data-driven moving vehicle model; since the mechanism model is established with some assumptions, some factors are ignored, and the discretization process is performed, there is an error between the vehicle mechanism model and the real vehicle; therefore, the mechanism model of the vehicle is combined with the data-driven modeling method to compensate for the error by using the data-driven method;

[0124] Let be the output of the mechanism and data-driven moving vehicle model at time k, and U(k) be the input of the mechanism and data-driven moving vehicle model at time k, be the model estimation error at time k+1; the mechanism model is a function related to U(k), which is represented as The error compensation model is a function related to U(k), which is represented as The error compensation model is a function related to U(k), which is represented as The error compensation model is a function related to U(k), which is represented as The mechanism and data-driven moving vehicle model is established as shown in formula (3):

[0125]

[0126] wherein, is the predicted output of the mechanism and data-driven moving vehicle model;

[0127] a-3). Establishment of ARX kinematic model; the time series ARX model is used to compensate for the error of the vehicle kinematic model, and the general structure of the ARX model of the output error of the kinematic model and the real vehicle is represented as follows:

[0128]

[0129] wherein, is the output error of the vehicle kinematic model at time k, U(k) = [v(k), δ f (k)] T is the input at time k; n a and n b correspond to the order of the output and input, respectively; A i (k+1) is a 3x3 matrix, B j (k+1) is a 3x2 matrix,

[0130]

[0131] wherein, A i (k+1), B j (k+1) are unknown parameters;

[0132] From the above, the motion vehicle model based on mechanism and data driving is represented as follows:

[0133]

[0134] a-4). Linearization of vehicle kinematic model; since there are nonlinear terms in the vehicle motion model established by formula (2), it is not conducive to the design and solution of the controller, therefore the nonlinear terms in formula (2) are linearized, and the linear form of formula (2) can be represented as:

[0135]

[0136] Wherein, Y(k+1) is the predicted output of the linearized vehicle kinematic model, Y(k) = [x(k), y(k), ψ(k)] T , is the output at k moment, U(k) = [v(k), δ f (k)] T , is the input at k moment, C(k) are the parameter matrix and time-varying constant term matrix after linearization of the model respectively;

[0137] The vehicle motion model represented by formula (2) is:

[0138]

[0139] Let g(v(k), δ f (k)) be the first-order Taylor expansion at (v(k-1), δ f (k-1)):

[0140]

[0141] Therefore, formula (7) can be represented as:

[0142]

[0143] Therefore C(k) is represented as follows:

[0144]

[0145]

[0146] b). Parameter estimation based on data-driven error compensation model; recursive least squares method is used to recursively estimate and identify the parameters in the system, and the parameter estimation is recursively corrected as new observation data is generated, until the parameter estimation reaches the required accuracy;

[0147] The parameter estimation based on data-driven error compensation model is realized through the following steps:

[0148] b-1). The least squares form of formula (4) is expressed as follows:

[0149]

[0150] Where φ(k) is the observed data vector, θ is the parameter vector to be estimated, and:

[0151]

[0152]

[0153] b-2). To prevent excessive parameter changes, a weighting term for parameter change is added to the recursive least squares forgetting factor method. η>0 is a weighting factor used to limit the change of the estimated parameters.

[0154] The performance indicators are as follows:

[0155]

[0156] make Then we can obtain:

[0157]

[0158] The least squares estimation problem of the parameters is to minimize the objective function (16) by finding the minimum value of J with respect to J. The first derivative of is set to zero, i.e.:

[0159]

[0160] By solving equation (16), we can obtain The value is given by the following formula:

[0161]

[0162] Let μ = β 2 If 0 < μ ≤ 1, then the least squares estimated parameters are... The solution is:

[0163]

[0164] make Discuss the factors in formula (18):

[0165] P -1 (k)=η-μη+μ·P -1 (k-1)+φ(k)φ T (k) (19)

[0166]

[0167] b-3). According to (18), the following formula can be obtained:

[0168]

[0169] Multiply both sides of formula (21) by The following formula can be obtained:

[0170]

[0171] Substitute (19) into (18) to obtain:

[0172]

[0173] Substitute (20) into formula (23) to obtain:

[0174]

[0175] Substitute (22) into formula (24) to obtain:

[0176]

[0177] Substitute (21) into formula (25) to obtain:

[0178]

[0179] The improved formula of the forgetting factor recursive least square parameter estimation is as follows:

[0180]

[0181] c). Adaptive path tracking controller design; the control objective is to minimize the position error between the vehicle and the reference path point, and the control inputs are the vehicle speed v and the front wheel steering angle δ f The controller for path tracking is achieved, wherein the position error includes the horizontal and vertical coordinate error and the heading angle error between the vehicle and the reference trajectory.

[0182] The adaptive path tracking controller design is achieved through the following steps:

[0183] c-1). The discrete model of the vehicle linear system can be expressed as:

[0184]

[0185] c-2). The change rate of the vehicle speed and the steering will affect the stability of the system, and therefore the change of the controller input needs to be limited; if the one-step forward prediction error criterion function is used, the control input solved by minimizing the function will be too large, and the controller cannot achieve the stable control of the system and the stability of the control system itself will also be destroyed; therefore, in order to solve the above problems, the following input criterion is designed:

[0186]

[0187] where λ>0 is a weight factor to limit the variation of the control input; Y * (k+1) is the target trajectory point and the desired heading angle, is the maximum vehicle speed and the front wheel steering angle;

[0188] c-3). Substituting equation (28) into equation (29) gives:

[0189]

[0190] Taking the derivative of equation (30) with respect to U(k) gives:

[0191]

[0192] In equation (31), The solution method is shown in equation (10) and equation (11), A i (k+1) is a 3x3 matrix, A i (k+1) is a 3x3 matrix, B i (k+1) is a 3x2 matrix, n a = 2, n b = 2, then we can get:

[0193]

[0194] Let then we can get:

[0195]

[0196] Further, the control rate can be obtained as equation (34):

[0197]

[0198] To verify the effectiveness of the adaptive control algorithm, scheme one compares the MFAC control algorithm and the MFAC algorithm based on coordinate compensation (model-free adaptive control algorithm) with the adaptive control algorithm based on the mechanism and data-driven vehicle motion model to verify the effectiveness of the adaptive control algorithm. Scheme two compares the anti-interference ability of the adaptive path tracking control and the path tracking control algorithm based on the coordinate compensation MFAC by adding disturbance to the measured data of the vehicle.

[0199] To verify the feasibility of the adaptive control scheme based on the mechanism and data-driven vehicle motion model, for the automatic marking vehicle path tracking control problem, the MFAC scheme and the MFAC scheme based on coordinate compensation are compared, and the simulation comparison experiments of the above three control schemes in the low-speed scene are given, and the path tracking effect is given. Considering that the automatic marking vehicle drives at low speed, therefore, the present application plans two target speed of 10km / h curve and straight line reference path.

[0200] As Figure 6 , 7, the path tracking based on MFAC has steady-state error, which is solved by the compensation target heading angle compensation algorithm. As Figure 8 , 9, compared Figure 4 , 5 can see that the adaptive path tracking controller designed in the present application does not have the problem of steady-state error, when tracking the straight line path from the deviation of 1m, it reaches the vicinity of the reference path at the longitudinal displacement of about 40m, and when the longitudinal displacement is about 60m, there is no obvious fluctuation. When tracking the curve path from the deviation of 1m, it reaches the vicinity of the reference path at the longitudinal displacement of about 40m, and when the longitudinal displacement is about 60m, there is no obvious fluctuation. Figure 8 , 9 can be seen, the MFAC path tracking control based on coordinate compensation reaches the vicinity of the reference path when tracking the straight line path from the deviation of 1m at the longitudinal displacement of about 180m. When tracking the curve path from the deviation of 1m, it reaches the vicinity of the reference path at the longitudinal displacement of about 180m. By comparison, it can be seen that the adaptive path tracking control algorithm designed in the present application has a faster response compared with the MFAC control algorithm.

[0201] In order to simulate the situation that the vehicle data receives disturbance and appears fluctuation, the path tracking effects of the adaptive control scheme based on the mechanism and data-driven vehicle motion model and the MFAC scheme based on coordinate compensation are compared, and the anti-interference ability of the two algorithms is analyzed.

[0202] The present application adds current data noise to the simulation real vehicle data output by the vehicle kinematics model at random time, so as to simulate the sensor data fluctuation caused by poor signal, electromagnetic interference and other factors in actual control. The experiment is designed as follows, the adaptive path tracking control scheme designed in the present application and the MFAC path tracking scheme based on coordinate compensation are used to track the curve path respectively. As Figure 10 、 11 shown, the path tracking deviation is as Figure 12 、 13 shown.

[0203] As Figure 10 , 11 shows that the path tracking effects of the two control schemes are good, and it is difficult to judge who is better, therefore, the path tracking control deviation is analyzed, asFigure 12 From the figure, it can be seen that the abscissa deviation of the adaptive path tracking control is much smaller than that of the MFAC path tracking control based on coordinate compensation, the ordinate deviation fluctuation of the adaptive path tracking control and the MFAC path tracking control based on coordinate compensation is similar, the vehicle heading angle deviation of the adaptive path tracking control is slightly smaller than that of the MFAC path tracking control based on coordinate compensation. Comprehensive analysis shows that the curve path tracking effect of the adaptive tracking control scheme designed in the application is better than that of the MFAC path tracking control scheme based on coordinate compensation.

[0204] The path tracking effects of the two control schemes after adding the interference are difficult to be directly judged from the path tracking effect diagram, so the tracking deviation of the vehicle is analyzed, as shown in Fig. Figure 14 , 15, it can be seen that the influence of the adaptive path tracking control on the abscissa and ordinate deviation before and after adding the noise is not obvious, and the fluctuation of the lateral angle is about 0.0015 rad. From Figure 15 , it can be seen that the influence of the MFAC path tracking control based on coordinate compensation on the abscissa and ordinate deviation before and after adding the noise is relatively obvious, and the fluctuation of the lateral angle is about 0.002 rad. The analysis of the controller output after adding the noise can directly reflect the influence of the noise on the controller, and then the stability and anti-interference ability of the controller can be analyzed. By comparing Figure 16 , 17, it can be seen that the output fluctuation of the adaptive path tracking control of the application after adding the noise is smaller, and the disturbance caused by the noise can be more quickly re-converged by the adaptive path tracking controller designed in the application. In summary, the anti-interference ability of the adaptive path tracking control scheme designed in the application is stronger.

Claims

1. A mechanism and data-driven model-based automatic striping car adaptive control method, characterized in that, The method is implemented by the following steps: a) establishment of a marking vehicle model based on mechanism and data driving; firstly, a kinematic model equation of the marking vehicle is established according to a mechanism model of the marking vehicle, then a vehicle motion model based on mechanism and data driving is established, and finally the vehicle motion model is linearized; b) parameter estimation of a data driving error compensation model; recursive least squares is used to recursively estimate and identify parameters in a system, and the parameter estimation is recursively corrected as new observation data is generated until the parameter estimation reaches a required accuracy; c). Adaptive path following controller design; to minimize the vehicle position and reference path point position error as the control objective, through the control of vehicle speed v and front wheel steering angle δ f A controller for path following is implemented, wherein the position error includes the lateral and longitudinal coordinate error and the heading angle error of the vehicle and the reference trajectory; The adaptive path tracking controller in step c) is designed by the following steps: c-1) the vehicle linear system discrete model can be expressed as: c-2) the vehicle speed and steering rate of change will affect the stability of the system, so the change of the controller input needs to be limited; if a one-step forward prediction error criterion function is used, the control input solved by minimizing the function will be too large, so the controller cannot achieve stable control of the system and the stability of the control system itself will be destroyed; therefore, to solve the above problem, the following input criterion is designed: where λ > 0 is a weighting factor to limit the variation of the control input; Y * (k+1) is the target trajectory point and the desired heading angle, is the maximum vehicle speed and the front wheel steering angle; c-3) substituting formula (28) into formula (29) gives: Taking the derivative of formula (30) with respect to U(k) gives: In formula (31), The solution method of C(k) is shown in formula (10) and formula (11), A i (k+1) is a 3*3 matrix, A i (k+1) is a 3*3 matrix, B i (k+1) is a 3*2 matrix, n a =2, n b =2, then the following can be obtained: Let Then we have: and the control rate can be obtained as formula (34): 2.The mechanism and data-driven model based automatic striping car adaptive control method of claim 1, wherein, The establishment of the marking vehicle model based on mechanism and data driving in step a) is implemented by the following steps: a-1). Establishing the kinematic equation of the marking vehicle; the front wheel of the marking vehicle is a steering wheel, the motion trajectory of the midpoint of the rear axle of the marking vehicle is selected to replace the motion trajectory of the vehicle, a plane coordinate system O-XY is established in the motion plane of the vehicle, x and y represent the horizontal coordinate and the vertical coordinate of the midpoint of the rear axle of the vehicle respectively, v represents the speed of the vehicle, ψ represents the body angle, δ f represents the front wheel turning angle, L represents the wheelbase between the front and rear wheels; the kinematic model equation of the marking vehicle is established as shown in formula (1): Since the microprocessor processes signals as digital signals in actual applications, the vehicle kinematic model in formula (1) is discretized: where T represents a control period; Based on the vehicle steering control mechanism, it is known that during actual parking, the front wheel steering angle will be affected by the maximum rotation angle of the front wheels. Due to the limitations, the front wheel steering angle in formula (2) must satisfy the following constraints: a-2) establishment of a vehicle motion model based on mechanism and data driving; since some assumptions are made in the establishment of the mechanism model, some factors are ignored, and the discretization is performed, so there is an error between the vehicle mechanism model and the actual vehicle; therefore, the vehicle mechanism model and the data driving modeling are combined, and the error is compensated by the data driving method; Let U(k) be the input to the mechanism and data driven moving vehicle model at time k, be the model estimation error at time k+1; then the mechanism model is a function of U(k) and is represented as the error compensation model is a function of U(k) and is represented as A mechanism and data driven moving vehicle model is established as shown in equation (3): In the formula, is the predicted output of the mechanism- and data-driven moving vehicle model; a-3) establishment of an ARX kinematic model; the time series ARX model is used to compensate the error of the vehicle kinematic model, and the general structure of the ARX model of the error between the kinematic model and the actual vehicle output is as follows: wherein, is the output error of the vehicle kinematic model at time k, U(k) = [v(k), δ f (k)] T is the input at time k; n a and n b correspond to the order of the output and input, respectively; A i (k+1) is a 3x3 matrix, B j (k+1) is a 3x2 matrix, wherein A i (k+1), B j (k+1) is an unknown parameter; According to the above, the vehicle motion model based on mechanism and data driving is expressed as: a-4) linearization of the vehicle kinematic model; since there are nonlinear terms in the vehicle motion model established in formula (2), it is not conducive to the design and solution of the controller, so the nonlinear terms in formula (2) are linearized, and the linear form of formula (2) can be expressed as: where Y(k + 1) is the predicted output of the linearized vehicle kinematic model, Y(k) = [x(k), y(k), ψ(k)] T , is the output at time k, U(k) = [v(k), δ f (k)] T is the input at time k, C(k) are the parameter matrix and time-varying constant matrix of the linearized model, respectively; The vehicle motion model established in formula (2) is expressed as: Let g(v(k),δ f (k)) be first order Taylor expanded about (v(k-1),δ f (k-1)): Therefore, formula (7) can be expressed as: So C(k) is expressed as follows: 3.The mechanism and data-driven model based automatic striping car adaptive control method of claim 2, wherein, The parameter estimation of the data driving error compensation model in step b) is implemented by the following steps: b-1) the least squares form of formula (4) is expressed as: where φ(k) is an observation data vector, θ is a parameter vector to be estimated, and b-2) to prevent the parameter from changing too much, a parameter change weight term is added to the recursive least squares forgetting factor method, η>0 is a weight factor for limiting the change of the estimated parameter; The performance index is taken as Let Then we have: The least square estimation problem of the parameters is to make the objective function (16) to be minimum, to get the first derivative of J about and let it be zero, that is: By solving the objective function (16), the value of is obtained as follows: Let μ = β 2 , 0 < μ ≤ 1, then the least squares estimate of the parameter is given by: Let The factor in equation (18) is discussed: P -1 (k) = η - μ + μ - P -1 (k - 1) + φ(k) φ T (k) (19) b-3). From (18) we have Equation (21) is multiplied by both sides by Equation (21) is multiplied by both sides by Substitute (19) into (18) to get Substitute (20) into (23) to get Substitute (22) into (24) to get Substitute (21) into (25) to get The improved recursive least square parameter estimation formula with the forgetting factor is as follows

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